scholarly journals Power series and asymptotic series associated with the Lerch zeta-function

1998 ◽  
Vol 74 (10) ◽  
pp. 167-170 ◽  
Author(s):  
Masanori Katsurada
Keyword(s):  
Power Series ◽  
Zeta Function ◽  
Asymptotic Series ◽  
Lerch Zeta Function

scholarly journals On some Lambert-like series

2020 ◽  
Vol Volume 42 - Special... ◽  
Author(s):  
P Agarwal ◽  
S Kanemitsu ◽  
T Kuzumaki
Keyword(s):  
Power Series ◽  
Zeta Function ◽  
Rational Function ◽  
Laurent Series ◽  
Zeta Functions ◽  
Limit Function ◽  
Lambert Series ◽  
Radial Limits ◽  
Lerch Zeta Function ◽  
International Audience

International audience In this note, we study radial limits of power and Laurent series which are related to the Lerch zeta-function or polylogarithm function. As has been pointed out in [CKK18], there have appeared many instances in which the imaginary part of the Lerch zeta-function was considered by eliminating the real part by considering the odd part only. Mordell studied the properties of the power series resembling Lambert series, and in particular considered whether the limit function is a rational function or not. Our main result is the elucidation of the threshold case of b_n = 1/n studied by Mordell [Mor63], revealing that his result is the odd part of Theorem 1.1 in view of the identities (1.9), (1.5). We also refer to Lambert series considered by Titchmarsh [Tit38] in connection with Estermann's zeta-functions.

scholarly journals Certain Integral Operator Related to the Hurwitz–Lerch Zeta Function

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xiao-Yuan Wang ◽  
Lei Shi ◽  
Zhi-Ren Wang
Keyword(s):  
Integral Operator ◽  
Zeta Function ◽  
Meromorphic Functions ◽  
Third Order ◽  
Lerch Zeta Function ◽  
Sandwich Type ◽  
Differential Superordination ◽  
Differential Subordinations

The aim of the present paper is to investigate several third-order differential subordinations, differential superordination properties, and sandwich-type theorems of an integral operator Ws,bf(z) involving the Hurwitz–Lerch Zeta function. We make some applications of the operator Ws,bf(z) for meromorphic functions.

scholarly journals Two-sided inequalities for the extended Hurwitz–Lerch Zeta function

2011 ◽  
Vol 62 (1) ◽  
pp. 516-522 ◽  
Author(s):  
H.M. Srivastava ◽  
Dragana Jankov ◽  
Tibor K. Pogány ◽  
R.K. Saxena
Keyword(s):  
Zeta Function ◽  
Lerch Zeta Function

scholarly journals A (p,v)-Extension of Hurwitz-Lerch Zeta Function and its Properties

2018 ◽  
Author(s):  
Gauhar Rahman ◽  
KS Nisar ◽  
Shahid Mubeen
Keyword(s):  
Zeta Function ◽  
Beta Function ◽  
Integral Representations ◽  
Basic Properties ◽  
Mellin Transformation ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
Generating Relations

In this paper, we define a (p,v)-extension of Hurwitz-Lerch Zeta function by considering an extension of beta function defined by Parmar et al. [J. Classical Anal. 11 (2017) 81–106]. We obtain its basic properties which include integral representations, Mellin transformation, derivative formulas and certain generating relations. Also, we establish the special cases of the main results.

scholarly journals Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

scholarly journals On extended Hurwitz–Lerch zeta function

2017 ◽  
Vol 448 (2) ◽  
pp. 1281-1304 ◽  
Author(s):  
Min-Jie Luo ◽  
Rakesh Kumar Parmar ◽  
Ravinder Krishna Raina
Keyword(s):  
Zeta Function ◽  
Lerch Zeta Function

scholarly journals Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 48
Author(s):  
Kottakkaran Sooppy Nisar
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Summation Formula ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function. To strengthen the main results we also consider some important special cases.

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